I'm not sure where the failure is happening.
1. I download the model I made in Autodesk Character Generator
2. I upload it to Mixamo to animate
3. After adding animations, I download from Mixamo with as FBX Unity with skin
4. I import into Unity, and the eyes do not show on the model, but the eyes are showing showing in the texture map.
I have the same issue in Unreal4 in UE4 you have to re apply your material map to the eyes.
I have the same problem in Unreal Engine 4, Maya, Blender, MotionBuilder, too. But I have solved the problem. After exporting to Unreal Engine 4, open the texture file in the content browser. You can see there is a material called "_Eye_trans", but its material isn't assigned. However, because the eye and the body are on the same material named "_Body". We can simply change the eyes' material to "_Body". Then you should see the eyes.